A163793 a(n) is the n-th J_13-prime (Josephus_13 prime).

5, 57, 117, 187, 251, 273, 275, 665, 2511, 40393, 48615, 755921, 970037

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 13th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_13-prime if this permutation consists of a single cycle of length N.

There are 13 J_13-primes in the interval 2..1000000 only. No formula is known; the J_13-primes have been found by exhaustive search.

References

R. L. Graham, D. E. Knuth & O. Patashnik, Concrete Mathematics (1989), Addison-Wesley, Reading, MA. Sections 1.3 & 3.3.

Links

Table of n, a(n) for n=1..13.

P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers, Discrete Applied Mathematics 159 (2011) 1915-1932.

P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology, 2014. University link.

Index entries for sequences related to the Josephus Problem

Example

All J_13-primes are odd.

Crossrefs

Cf. A163782 through A163792 for J_2- through J_12-primes.

Cf. A163794 through A163800 for J_14- through J_20-primes.

Sequence in context: A336243 A356134 A363059 * A226425 A076455 A196650

Adjacent sequences: A163790 A163791 A163792 * A163794 A163795 A163796

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 04 2009

Status

approved